This paper is concerned with the existence of solutions for a kind of nonhomogeneous critical p-Kirchhoff type problem driven by an integro-differential operator L p K . In particular, we investigate the equation: M �ZZ R2n |v(x) − v(y)| p |x − y| n+ps dxdy� L p K v(x) = µg(x)|v| q−2 v + |v| p s −2 v + µ f(x) in R n where g(x) > 0, and f(x) may change sign, µ > 0 is a real parameter, 0 ps, 1 < q < p < p s , p s = np n−ps is the critical exponent of the fractional Sobolev space W s,p K (Rn ). By exploiting Ekeland’s variational principle, we show the existence of non-trivial solutions. The main feature and difficulty of this paper is the fact that M may be zero and lack of compactness at critical level L p s (Rn Our conclusions improve the related results on this topic
